Circle Calculator

How it works

A circle is fixed by a single number, its radius. The diameter is twice the radius, the circumference is 2π times the radius, and the area is π times the radius squared. Because each of these is a one-to-one function of the radius, knowing any one of them fixes the other three.

The calculator first turns whatever you entered back into a radius: half the diameter, the circumference divided by 2π, or the square root of the area divided by π. It then computes the other three from that radius.

The unit you pick labels the results and does not convert anything. Enter the measurement in that unit and the lengths come out in it, the area in it squared.

Formula

diameter      = 2 × r
circumference = 2 × π × r
area          = π × r²
r from diameter      = d ÷ 2
r from circumference = C ÷ (2π)
r from area          = √(A ÷ π)

Example

A circle with a 5 ft radius has a diameter of 10 ft, a circumference of 2 × π × 5 ≈ 31.42 ft, and an area of π × 25 ≈ 78.54 ft².

Working back from an area of 100 ft², the radius is √(100 ÷ π) ≈ 5.64 ft, the diameter ≈ 11.28 ft and the circumference ≈ 35.45 ft.

Assumptions and limitations

• The shape is a true circle. An ellipse, or a tank or pipe that is slightly out of round, has a different area for the same longest diameter.
• The measurement is in the unit you choose; the unit labels the result and does not convert anything.
• π is used to full double precision, not 3.14 or 22/7, so the last digits may differ from a hand calculation that rounds π.
• Results are rounded for display only.

Frequently asked questions